Answer:
To find the values of a and b, we solve the system of linear equations by subtracting the first from the second, finding that b = 0, then solving for a, which is expressed in terms of EG as a = (EG - 2) / 2.
Step-by-step explanation:
To solve the system of linear equations for the variables a and b, we are given the following two equations:
- EG = 2a + 3b + 2
- FH = 2a + 3 + 6b - 1
We can simplify the second equation to make it easier to work with:
- EG = 2a + 3b + 2 (Equation 1)
- FH = 2a + 6b + 2 (Equation 2)
Next, subtract Equation 1 from Equation 2 to eliminate a, yielding:
- 0 = 3b - 3b + 6b - 3b + 2 - 2
- 0 = 3b
This leaves us with a solution for b: b = 0. We can then substitute b back into either Equation 1 or Equation 2 to solve for a:
- EG = 2a + 3(0) + 2
- EG = 2a + 2
- a = (EG - 2) / 2
To find specific values for EG and FH, we would need their numerical values. Without those, we can only express a in terms of EG, and we've already determined that b equals 0.